Optical systems such as monoculars, binoculars, telescopes, microscopes, cameras and projectors are composed of various arrangements of converging and diverging lenses. For example, typical optical systems employ compound lenses which are a one-dimensional array of simple convex or concave lenses with a common optical axis. Some of these optical systems produce a virtual image when viewed by the human eye, while others produce a real image that can be captured on photographic film or an optical sensor, or can be viewed on a screen.
However, conventional lenses typically do not form perfect images. In particular, there is nearly always at least some degree of image distortion or aberration introduced by even carefully manufactured lenses. Aberrations can be reduced by meticulously positioning, shaping, and polishing the lenses of an optical system, but this in turn increases the cost of manufacturing the optical system. Designers and manufacturers of optical systems also attempt to compensate for distortions and aberrations by fabricating compound lenses composed of simple lenses configured with complementary distortions or aberrations. However, this method of manufacturing optical systems can also be costly and time consuming.
Designers and manufacturers of optical systems continue to seek enhancements in lens design and lens manufacturing techniques.